The following picture shows two vectors as well as the parallelogram that is spanned by them.
The area of a parallelogram is simply the length times the height. In this case, the length of the parallelogram is and the height is . Thus, the area is . Very often it is helpful to think of the area as a vector. The magnitude of the area vector is simply the ordinary area. Its direction is perpendicular to the surface itself. Thus, the area vector for the parallelogram above would point out of the screen.